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If you are adding and
subtracting fractions with unlike
denominators, the first thing you need to do is to find a
common denominator.
Fractions
with different denominators
can be compared
by changing them to an
equivalent fraction with a common denominator.
A Common Denominator
is when two fractions have the
same denominator.
To
start: Find the Least
Common Multiple
(LCM)
of your two denominators.
Ex: 3/4
- 2/3
=
4= 4, 8, 12,
16, ...
3 = 3, 6, 9, 12
12 is the LCM
3
x3/4
x3
= 9/12
2 x4/3
x4
= 8/12
so...
3/4
can also be 9/12
and
2/3
can also be 8/12
Then:
Subtract
the
NEW
numerators (top number of fraction)
to determine =
9
- 8 = 1
so...
9/12
- 8/12
= 1/12
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Example:
Adding Fractions with Unlike Denominators:
2/5
+
1/4
Step 1: Find a
common denominator
5=
5, 10, 15, 20,
25, ...
4= 4, 8, 12, 16, 20
LCM= 20
Step 2: Write
equivalent fractions
2
x4/5
x4
= 8/20
1
x5/4
x5
= 5/20
Step 3: Add
the numerators. Simplify if possible.
8 + 5
= 13 so...
8/20 +
5/20 =
13/20
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Example: Subtracting Fractions with Unlike Denominators:
1/2
-
2/7
Step 1: Find
a common denominator
2=
2, 4, 6, 8,
10, 12, 14,
16...
7= 7, 14
LCM= 14
Step 2: Write equivalent fractions
1
x7/2
x7
= 7/14
2
x2/7
x2
= 4/14
Step 3:
Subtract the numerators. Simplify if possible.
7
- 4 =
3 so...
7/14 - 4/14 =
3/14 |
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Example: Adding Fractions with Unlike Denominators:
3/5
+
1/3
Step 1: Find
a common denominator
5=
5, 10, 15,
20, ...
3= 3, 6, 9, 12, 15
LCM= 15
Step 2:
Write equivalent fractions
3
x3/5
x3
= 9/15
1
x5/3
x5
= 5/15
Step 3: Add
the numerators. Simplify if possible.
9
+ 5
= 14, so...
9/15 +
5/15
=
14/15
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Remember:
Fractions
that have unlike denominators
can be added or subtracted by finding the common denominator.
Then add or
subtract the numerators,
simplify if possible.
Let's Practice
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